Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Complexity theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Predictive Complexity of Quantum Subsystems

We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of predictive state analysis of stochastic and complex systems theory but is intrinsically quantum. Predictive states of a subsystem are formed by equivalence classes of state vectors in the exterior Hilbert space that effectively predict the same future behavior of that subsystem for some time. As an illustrative example, we present calculations in the dynamics of an isotropic Heisenberg model spin chain and show that, in comparison to the entanglement entropy, the predictive complexity better signifies dynamically important events, such as magnon collisions. It can also serve as a local order parameter that can distinguish long and short range entanglement.

Asplund, Curtis T. (ORCID:0000000305575850)↗
DOE OSTI2025

Quantum Algorithms for Representation-Theoretic Multiplicities

Kostka, Littlewood-Richardson, Plethysm, and Kronecker coefficients are the multiplicities of irreducible representations in the decomposition of representations of the symmetric group that play an important role in representation theory, geometric complexity, and algebraic combinatorics. We give quantum algorithms for computing these coefficients whenever the ratio of dimensions of the representations is polynomial. We show that there is an efficient classical algorithm for computing the Kostka numbers under this restriction and conjecture the existence of an analogous algorithm for the Littlewood-Richardson coefficients. We argue why such classical algorithm does not straightforwardly work for the Plethysm and Kronecker coefficients and conjecture that our quantum algorithms lead to superpolynomial speedups. The conjecture about Kronecker coefficients was disproved by Panova [Polynomial time classical versus quantum algorithms for representation theoretic multiplicities, arXiv:2502.20253] with a classical algorithm which, if optimal, points to a 𝒪⁡(𝑛 4+2⁢𝑘 ) vs $\tilde{Ω}$⁡(𝑛 4⁢𝑘 2 +1 ) polynomial gap in quantum vs classical computational complexity for an integer parameter 𝑘.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Low-Order Preconditioning for the High-Order Finite Element de Rham Complex

Here, we present a unified framework for constructing spectrally equivalent low-order-refined discretizations for the high-order finite element de Rham complex. This theory covers diffusion problems in H 1 , H(curl), and H(div) and is based on combining a low-order discretization posed on a refined mesh with a high-order basis for Nédélec and Raviart–Thomas elements that makes use of the concept of polynomial histopolation (polynomial fitting using prescribed mean values over certain regions). This spectral equivalence, coupled with algebraic multigrid methods constructed using the low-order discretization, results in highly scalable matrix-free preconditioners for high-order finite element problems in the full de Rham complex. Additionally, a new lowest-order (piecewise constant) preconditioner is developed for high-order interior penalty discontinuous Galerkin (DG) discretizations, for which spectral equivalence results and convergence proofs for algebraic multigrid methods are provided. In all cases, the spectral equivalence results are independent of polynomial degree and mesh size; for DG methods, they are also independent of the penalty parameter. These new solvers are flexible and easy to use; any “black-box” preconditioner for low-order problems can be used to create an effective and efficient preconditioner for the corresponding high-order problem. A number of numerical experiments are presented, based on an implementation in the finite element library MFEM. A range of challenging three-dimensional problems are used to corroborate the theoretical properties and demonstrate the flexibility and scalability of the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Electronic structure analysis and DFT benchmarking of Rydberg-type alkali-metal-crown ether, -cryptand, and -adamanzane complexes

Density functional theory (DFT) and electron propagator theory (EPT) calculations were performed to study ground and excited electronic structures of alkali-metal (M) coordinated 9-crown-3, 24-crown-8, [2.1.1]cryptand, o-Me 2 -1.1.1, and 3 6 Adamanzane complexes. Each complex bears an expanded electron in the periphery and occupies diffuse 1p-, 1d-, 1f-type molecular orbitals (or superatomic 1P, 1D, 1F orbitals) in excited electronic states. The calculated superatomic shell model of the M(9-crown-3) 2 is 1S, 1P, 1D, 1F, 2S, 2P, 2D, 1G and it is held by all other complexes up to the studied 1F level. Due to the highly diffuse nature of the electron, the ionization energies of these complexes are significantly lower (1.6–2.0 eV) and hence these complexes belong to the superalkali category. Further, the ab initio EPT ionization energy and the excitation energies of the Li(9-crown-3) 2 were used to evaluate DFT errors associated with a series of exchange correlation functionals that span multiple rungs of Jacob's ladder (i.e., GGA, meta-GGA, global GGA hybrid, meta-GGA hybrid, range-separated hybrid, double-hybrid). Among these, the best performing functional is the range-separated hybrid CAM-B3LYP and the errors are within 6% of high-level ab initio EPT results. The accuracy of CAM-B3LYP is indeed transferable to similar complexes and hence the findings are expected to accelerate the progression of studies of Rydberg-type systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Exotic phases in finite-density ℤ 3 theories

Lattice ℤ 3 theories with complex actions share many key features with finite- density QCD including a sign problem and $\mathcal{CK}$ symmetry. Complex ℤ 3 spin and gauge models exhibit a generalized Kramers-Wannier duality mapping them onto chiral ℤ 3 spin and gauge models, which are simulatable with standard lattice methods in large regions of parameter space. The Migdal-Kadanoff real-space renormalization group (RG) preserves this duality, and we use it to compute the approximate phase diagram of both spin and gauge ℤ 3 models in dimensions one through four. Chiral ℤ 3 spin models are known to exhibit a Devil’s Flower phase structure, with inhomogeneous phases that can be thought of as ℤ 3 analogues of chiral spirals. Out of the large class of models we study, we find that only chiral spin models and their duals have a Devil’s Flower structure with an infinite set of inhomogeneous phases, a result we attribute to Elitzur’s theorem. We also find that different forms of the Migdal-Kadanoff RG produce different numbers of phases, a violation of the expectation for universal behavior from a real-space RG. We discuss extensions of our work to ℤ N models, SU(N) models and nonzero temperature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

A highly stable Cu(OH) 2 -Poly(vinyl alcohol) nanocomposite membrane for dramatically enhanced direct borohydride fuel cell performance

Nano-additive aggregation, limited performance, and unclear modification mechanisms are the main obstacles in developing nanocomposite anion exchange membranes (AEMs). In this work, for the first time, an effective and highly stable Poly(vinyl alcohol) (PVA)-based AEMs with dispersive Cu(OH)$_2$ nanoclusters (Cu-AEMs) are prepared by a simple and eco-friendly three-step method: ‘CuCl$_2$ doping-casting-KOH immersing’. The doped Cu$^{2+}$ ions chemically combine with OH- ions to form anionic conductive Cu(OH)2 nanoclusters intermediated by attaching resins. The PVA skeletons wrap around Cu(OH)$_2$ while the hydroxyl groups expose to bulk water, forming Cu(OH)$_2$-PVA complex, which avoids nano-additive aggregation, increases anionic channels, and strengthens additive-matrix connection. A direct borohydride fuel cell using Cu-AEM with 0.56 wt % CuCl$_2$ possess the highest power density of 403.3 mW cm$^{-2}$ at 60 °C and a life span of over 200 h. The high-performance and durability come from the unique structure of Cu(OH)$_2$ nanoclusters-PVA complex. ‘Vehicle’ theory is considered to be the dominant mechanism for enhancing such nanocomposite Cu-AEMs. This work demonstrates a new concept for preparing the stable AEMs toward high-performance fuel cells. The synthetic chemistry involved can be broadly extended for fabricating versatile AEMs.

25 ENERGY STORAGE↗
DOE OSTI2024

Frontiers in Scientific Workflows: Pervasive Integration With High-Performance Computing

Herein we address the increasing complexity of scientific workflows in the context of high-performance computing (HPC) and their associated need for robust, adaptable, and flexible computational support systems. We explore five key trends as well as future challenges and opportunities for scientific workflows and HPC technologies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Structured Adaptive Mesh Refinement Adaptations to Retain Performance Portability With Increasing Heterogeneity

Adaptive mesh refinement (AMR) is an important method that enables many mesh-based applications to run at effectively higher resolution within limited computing resources by allowing high resolution only where really needed. This advantage comes at a cost, however: greater complexity in the mesh management machinery and challenges with load distribution. With the current trend of increasing heterogeneity in hardware architecture, AMR presents an orthogonal axis of complexity. Additionally, the usual techniques, such as asynchronous communication and hierarchy management for parallelism and memory that are necessary to obtain reasonable performance are very challenging to reason about with AMR. Different groups working with AMR are bringing different approaches to this challenge. Here, we examine the design choices of several AMR codes and also the degree to which demands placed on them by their users influence these choices.

42 ENGINEERING↗
DOE OSTI2024

Enhancing Distribution System Resilience: A First-Order Meta-RL Algorithm for Critical Load Restoration

The increasing frequency of extreme events and the integration of distributed energy resources (DERs) into modern grids have elevated the need for resilient and efficient critical load restoration strategies in distribution systems. However, the stochastic nature of renewable DERs, limited energy resource availability and the intricate nonlinearities inherent in complex grid control problem make the problem challenging. Although reinforcement learning (RL) and warm-start RL methods have shown promising results, their performance often falls short in rapidly adapting to new, unseen situations and typically requires exhaustive problem-specific tuning. To address these gaps, we propose a First-Order Meta-based RL (FOM-RL) algorithm within an online framework for adaptive and robust critical load restoration. By harnessing local DERs as the enabling technology, FOM-RL allows the RL agent to swiftly adapt to new unseen scenarios by leveraging previously acquired knowledge of different tasks. Experimental results provide evidence that proposed algorithm learns more efficiently and showcases generalization capabilities across diverse set of operational scenarios. Moreover, a rigorous theoretical analysis yields a tight sublinear regret bound, sensitive to temporal variability, with a task-averaged optimality gap bounded by O(VM+D*/(Tsquare root(M))). These results suggest that optimality improves with task similarity and an increased number of tasks M, reaffirming the efficacy and scalability of the proposed approach in addressing the complexities of critical load restoration in distribution systems.

complexity theory↗
DOE OSTI2022

Quantum Distributed Unit Commitment: An Application in Microgrids

The dawn of quantum computing brings on a revolution in the way combinatorially complex power system problems such as Unit Commitment are solved. The Unit Commitment problem complexity is expected to increase in the future because of the trend toward the increase of penetration of intermittent renewables. Even though quantum computing has proven effective for solving a host of problems, its applications for power systems’ problems have been rather limited. Here, in this paper, a quantum unit commitment is innovatively formulated and the quantum version of the decomposition and coordination alternate direction method of multipliers (ADMM) is established. The above is achieved by devising quantum algorithms and by exploiting the superposition and entanglement of quantum bits (qubits) for solving subproblems, which are then coordinated through ADMM to obtain feasible solutions. The main contributions of this paper include: 1) the innovative development of a quantum model for Unit Commitment; 2) development of decomposition and coordination-supported framework which paves the way for the utilization of limited quantum resources to potentially solve the large-scale discrete optimization problems; 3) devising the novel quantum distributed unit commitment (QDUC) to solve the problem in a larger scale than currently available quantum computers are capable of solving. The QDUC results are compared with those from its classical counterpart, which validate the efficacy of quantum computing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Activity Theory Literature Review

Complex challenges across Sandia National Laboratories' (SNL) mission areas underscore the need for systems level thinking, resulting in a better understanding of the organizational work systems and environments in which our hardware and software will be used. SNL researchers have successfully used Activity Theory (AT) as a framework to clarify work systems, informing product design, delivery, acceptance, and use. To increase familiarity with AT, a working group assembled to select key resources on the topic and generate an annotated bibliography. The resources in this bibliography are arranged in six categories: 1) An introduction to AT; 2) Advanced readings in AT; 3) AT and human computer interaction (HCI); 4) Methodological resources for practitioners; 5) Case studies; and 6) Related frameworks that have been used to study work systems. This annotated bibliography is expected to improve the reader's understanding of AT and enable more efficient and effective application of it.

42 ENGINEERING↗
DOE OSTI2024

Theories of homogeneous and electrochemical electron transfer in complex media and interfaces (Final Technical Report)

This project makes the next step in establishing practical theories of charge transfer in complex media. The development of formal models is supported by extensive atomistic simulations, quantum calculations of force-field parameters, and direct measurements of charge-transfer spectra. All theory development is supported by experiment, extensive numerical simulations, and through external collaborations.

14 SOLAR ENERGY↗
DOE OSTI2023

Three-body resonances in the φ 4 theory

We study the properties of three-body resonances using a lattice complex scalar φ4 theory with two scalars, with parameters chosen such that one heavy particle can decay into three light ones. We determine the two- and three-body spectra for several lattice volumes using variational techniques, and then analyze them with two versions of the three-particle finite-volume formalism: the Relativistic Field Theory approach and the Finite-Volume Unitarity approach. We find that both methods provide an equivalent description of the energy levels, and we are able to fit the spectra using simple parametrizations of the scattering quantities. By solving the integral equations of the corresponding three-particle formalisms, we determine the pole position of the resonance in the complex energy plane and thereby its mass and width. We find very good agreement between the two methods at different values of the coupling of the theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

X-ray absorption spectra of f-element complexes: insight from relativistic multiconfigurational wavefunction theory

X-ray absorption near edge structure (XANES) spectroscopy, coupled with ab initio calculations, has emerged as the state-of-the-art tool for elucidating the metal-ligand bonding in f-element complexes. Furthermore, this highlight presents recent efforts in calculating XANES spectra of lanthanide and actinide compounds with relativistic multiconfiguration wavefunction approaches that account for differences in donation bonding in the ground state (GS) versus a core-excited state (ES), multiplet effects, and spin-orbit-coupling. With the GS and ES wavefunctions available, including spin-orbit effects, an arsenal of chemical bonding tools that are popular among chemists can be applied to rationalize the observed intensities in terms of covalent bonding.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Binding of carboxylate and water to monovalent cations

The interactions of carboxylate anions with water and cations are important for a wide variety of systems, both biological and synthetic. Here, in order to gain insight on properties of the local complexes, we apply density functional theory, to treat the complex electrostatic interactions, and investigate mixtures with varied numbers of carboxylate anions (acetate) and waters binding to monovalent cations, Li + , Na + and K + . The optimal structure with overall lowest free energy contains two acetates and two waters such that the cation is four-fold coordinated, similar to structures found earlier for pure water or pure carboxylate ligands. More generally, the complexes with two acetates have the lowest free energy. In transitioning from the overall optimal state, exchanging an acetate for water has a lower free energy barrier than exchanging water for an acetate. In most cases, the carboxylates are monodentate and in the first solvation shell. As water is added to the system, hydrogen bonding between waters and carboxylate O atoms further stabilizes monodentate structures. These structures, which have strong electrostatic interactions that involve hydrogen bonds of varying strength, are significantly polarized, with ChelpG partial charges that vary substantially as the bonding geometry varies. Overall, these results emphasize the increasing importance of water as a component of binding sites as the number of ligands increases, thus affecting the preferential solvation of specific metal ions and clarifying Hofmeister effects. Finally, structural analysis correlated with free energy analysis supports the idea that binding to more than the preferred number of carboxylates under architectural constraints are a key to ion transport.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Low-cost calculation and analysis of 2D IR spectra of model diiron trinitrosyl complexes in the NO stretch region with vibrational perturbation theory

Two-dimensional infrared spectroscopy offers unique capabilities for probing vibrational coupling in complex metal–ligand systems. In this paper, we combine two-dimensional infrared spectroscopy with vibrational perturbation theory to investigate vibrational coupling in a diiron trinitrosyl complex across three stable redox states. Although these systems are challenging for electronic structure methods, we demonstrate that key features of experimental 2D IR spectra can be accurately reproduced using reduced-dimensional anharmonic calculations with a small harmonic frequency scaling. Analysis reveals that N–O stretching modes maintain high locality across all redox states, with coupling patterns that directly reflect variations in Fe–N bond strength. Using curvilinear coordinate analysis, we demonstrate these differences result from systematic changes in cubic anharmonic force constants rather than mode delocalization. Our results establish N–O stretches as sensitive probes of metal–ligand bonding strength, expanding the toolkit for studying biologically relevant nitrosyl complexes.

Moran, Hayden A. [Texas A&M University, College St↗
DOE OSTI2022

Integrating out beyond tree level and relativistic superfluids

We revisit certain subtleties of renormalization that arise when one derives a low-energy effective action by integrating out the heavy fields of a more complete theory. Usually these subtleties are circumvented by matching some physical observables, such as scattering amplitudes, but a more involved procedure is required if one is interested in deriving the effective theory to all orders in the light fields (but still to fixed order in the derivative expansion). As a concrete example, we study the U(1) Goldstone low-energy effective theory that describes the spontaneously broken phase of a $\phi$ 4 theory for a complex scalar. Working to lowest order in the derivative expansion, but to all orders in the Goldstones, we integrate out the radial mode at one loop and express the low-energy effective action in terms of the renormalized couplings of the UV completion. This yields the one-loop equation of state for the superfluid phase of (complex) $\phi$ 4 . We perform the same analysis for a renormalizable scalar SO(N) theory at finite chemical potential, integrating out the gapped Goldstones as well, and confirm that the effective theory for the gapless Goldstone exhibits no obvious sign of the original SO(N) symmetry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗